Oriented Matroids
Oriented matroids appear throughout discrete geometry, with applications in algebra, topology, physics, and data analysis. This introduction to oriented matroids is intended for graduate students, scientists wanting to apply oriented matroids, and researchers in pure mathematics. The presentation is geometrically motivated and largely self-contained, and no knowledge of matroid theory is assumed. Beginning with geometric motivation grounded in linear algebra, the first chapters prove the major cryptomorphisms and the Topological Representation Theorem. From there the book uses basic topology to go directly from geometric intuition to rigorous discussion, avoiding the need for wider background knowledge. Topics include strong and weak maps, localizations and extensions, the Euclidean property and non-Euclidean properties, the Universality Theorem, convex polytopes, and triangulations. Themes that run throughout include the interplay between combinatorics, geometry, and topology, and the idea of oriented matroids as analogs to vector spaces over the real numbers and how this analogy plays out topologically.
2023-2024 Elementary School Contest Materials
This book contains one year of mathleague.org elementary school tests and answer keys: 7 qualifying-level test sets, one state-level test set, one national-level test set, and one international-level. Each test set contains a Sprint, Target, Team, and Number Sense test.
Discrete Mathematics for Engineering
Discrete Mathematics is an essential paper to discuss not only in mathematics but also in Engineering Departments. Mostly Computer Science and Engineering. We can thing that in higher secondary we are learning Set Theory, Functions, Relations and some others. After that this mathematics goes to logical representation as Discrete Mathematics and after a while Digital Logic is persued. So if I thinking to a computer we need to know it's mathematics that is Discrete Mathematics.
Logic for Dummies
An accessible resource to help you puzzle out logic concepts Logic For Dummies, 2nd Edition explains all the varied ways we use logic in philosophy, science, and everyday life. College students taking a logic course and lifelong learners alike can benefit from this accessible guide to logic concepts--such as syllogisms, constructing proofs and refutations, propositional and predicate logic, symbolic logic, modal and fuzzy logic, deductive and inductive reasoning, and beyond. With real-world examples, fun logic problems, and fully worked out proofs, you have plenty of opportunities to follow along and apply what you've learned. Logic For Dummies, 2nd Edition helps you connect the logical dots! Inside: Grasp formal and informal logic with clear explanations and practice problems See how logic shows up in everyday life and discover how to spot logical fallacies Work through logical proofs and refutations, with answer explanations to strengthen your understanding Sharpen your ability to reason through complex issues with truth tables Logic For Dummies, 2nd Edition is the logical choice for anyone who wants or needs to learn the concepts, theories, and formulas of logical reasoning.
Applications of SET Theory and Relations & Functions in fields of CSE
SET theory is a basic concepts of mathematics. And we can say Computer Science and Engineering has built up by mathematics. By SET theory we can describe the mathematical model of Theory of Computation. How can have an idea how does an algorithm can be build. Discrete Mathematics has a strong connection between SET Theory, Relations and Functions. Now I discuss about Database Management System then SET theory has a crucial role to play. Have nice nice journey with this book.
Introduction to Qualitative Methods for Differential Equations
Introduction to Qualitative Methods for Differential Equations provides an alternative approach to teaching and understanding differential equations. The basic methodology of the book is centred on finding reformulations of differential equations in such a manner that they become (partially, at least) problems in geometry. Through this approach, the book distils the critical aspects of the qualitative theory of differential equations and illustrates their application to a number of nontrivial problems.Features Self-contained with suggestions for further reading Concise and approachable exposition with only minimal pre-requisites Ideal for self-study Appropriate for undergraduate mathematicians, engineers, and other quantitative science students.
A Mathematical Tour
A Mathematical Tour introduces readers to a selection of mathematical topics chosen for their centrality, importance, historical significance, and intrinsic appeal and beauty. The book is written to be accessible and interesting to readers with a good grounding in high school level mathematics and a keen sense of intellectual curiosity. Each chapter includes a short history of the topic, statements and discussion of important results, illustrations, user-friendly exercises, and suggestions for further reading. This book is intended to be read for pleasure but could also be used for a Topics course in Mathematics or as a supplementary text in a History of Mathematics course.Features- contains a selection of accessible mathematical topics- exercises that elucidate, and sometimes enlarge on, the topics- suitable for readers with knowledge of high school mathematics
The Doctrine of Triangles
An interdisciplinary history of trigonometry from the mid-sixteenth century to the early twentieth The Doctrine of Triangles offers an interdisciplinary history of trigonometry that spans four centuries, starting in 1550 and concluding in the 1900s. Glen Van Brummelen tells the story of trigonometry as it evolved from an instrument for understanding the heavens to a practical tool, used in fields such as surveying and navigation. In Europe, China, and America, trigonometry aided and was itself transformed by concurrent mathematical revolutions, as well as the rise of science and technology. Following its uses in mid-sixteenth-century Europe as the "foot of the ladder to the stars" and the mathematical helpmate of astronomy, trigonometry became a ubiquitous tool for modeling various phenomena, including animal populations and sound waves. In the late sixteenth century, trigonometry increasingly entered the physical world through the practical disciplines, and its societal reach expanded with the invention of logarithms. Calculus shifted mathematical reasoning from geometric to algebraic patterns of thought, and trigonometry's participation in this new mathematical analysis grew, encouraging such innovations as complex numbers and non-Euclidean geometry. Meanwhile in China, trigonometry was evolving rapidly too, sometimes merging with indigenous forms of knowledge, and with Western discoveries. In the nineteenth century, trigonometry became even more integral to science and industry as a fundamental part of the science and engineering toolbox, and a staple subject in high school classrooms. A masterful combination of scholarly rigor and compelling narrative, The Doctrine of Triangles brings trigonometry's rich historical past full circle into the modern era.
A Mathematical Tour
A Mathematical Tour introduces readers to a selection of mathematical topics chosen for their centrality, importance, historical significance, and intrinsic appeal and beauty.
Engaging Young Student Math (V3)
Engaging Young Students in Mathematics through Competitions presents a wide range of topics relating to mathematics competitions and their meaning in the world of mathematical research, teaching and entertainment. Following the earlier two volumes, contributors explore a wide variety of fascinating problems of the type often presented at mathematics competitions. In this new third volume, many chapters are directly related to the challenges involved in organizing competitions under Covid-19, including many positive aspects resulting from the transition to online formats. There are also sections devoted to background information on connections between the mathematics of competitions and their organization, as well as the competitions' interplay with research, teaching and more.The various chapters are written by an international group of authors involved in problem development, many of whom were participants of the 9th Congress of the World Federation of National Mathematics Competitions in Bulgaria in 2022. Together, they provide a deep sense of the issues involved in creating such problems for competition mathematics and recreational mathematics.
Amusements in Mathematics
Unlock the Enigma of Numbers with a Timeless Classic! Dive into the captivating world of ""Amusements in Mathematics"" by the legendary Henry Ernest Dudeney, a masterpiece that has enchanted puzzle enthusiasts for generations. This extraordinary collection of mathematical puzzles and brainteasers, once out of print for decades, is now beautifully republished by Alpha Editions, making it a must-have collector's edition for both the curious minds of today and the inquisitive thinkers of tomorrow. From mind-bending riddles to ingenious conundrums, Dudeney's brilliance shines through every page, offering a delightful challenge to both novice and seasoned puzzle solvers. Whether you're looking to sharpen your problem-solving skills or simply seeking an entertaining escape into the world of numbers, this book promises hours of intellectual amusement. Don't miss your chance to own a piece of mathematical history that has stood the test of time. Rediscover the joy of puzzles with ""Amusements in Mathematics"" and let your imagination soar!
Proceedings on Non Commutative Geometry
This book deals with generalizations of topology and in particular metricity. Given that those subjects arise out of Boolean logic, we diligently present this material first. Later on, quantal logic is studied as well as generalizations thereof. This leads to the study of simple quantum geometries such as the non commutative simplex. Furthermore, generalizations of classical geometry are presented leading to the notion of a quantal metric space attached to a classical one.
Course in Ordinary Differential Equations with Applications
This book was written for advanced undergraduate math or science majors. Its initial purpose was to illustrate the elementary mathematical theory of ordinary differential equations and their diverse and powerful applications. Historically these have been decisive in many physical problems, some of which have philosophically challenged and indeed altered our civilization's concepts. Because of the importance of the subject, the book is also suitable for a one-semester course for graduate students. The book consists of 12 chapters and six appendices.
Mathematics to Abstract Machine, Then Physical Computer
Computer Science and Engineering is a huge part of society. If we go through very minutely about where from Computer is coming. We can say Computer is an application of Mathematics. Firstly, we have discussed K12 Mathematics at basic world accepted level, then I had to do Mathematics at graduate level. There I have found digital computation. When I am discussing about Discrete Mathematics then it's along with Theory of Computation. Then Digital electrics has been designed in a simulation form. After that, we have gone to physical design of Computer System that is nothing but Computer Architecture.
Select Ideas in Partial Differential Equations
This book provides a concise but thorough introduction to partial differential equations which model phenomena that vary in both space and time. The author begins with a full explanation of the fundamental linear partial differential equations of physics. The text continues with methods to understand and solve these equations leading ultimately to the solutions of Maxwell's equations. The author then addresses nonlinearity and provides examples of separation of variables, linearizing change of variables, inverse scattering transform, and numerical methods for select nonlinear equations. Next, the book presents rich sources of advanced techniques and strategies for the study of nonlinear partial differential equations. This second edition includes updates, additional examples, and a new chapter on reaction-diffusion equations. Ultimately, this book is an essential resource for readers in applied mathematics, physics, chemistry, biology, and engineering who are interested in learning about the myriad techniques that have been developed to model and solve linear and nonlinear partial differential equations.
Jewish Calendar Mathematics
This book begins with a short overview of calendars in general, and then delves deeply into Jewish calendar structure and mathematics. Details of how Torah portions are scheduled and how the structured triennial Torah reading and haftorah reading cycles work are explained. A comprehensive explanation of the calendrical aspects of Jewish holidays as well as the relationships between them and non-Jewish holidays is included. There are fourten appendices which allow even greater visibility into the material than does the main narrative by itself. This volume also includes substantial new material absent from the book's predecessor. A glossary is provided.
A Complete Hand Book for Higher Secondary Mathematics
Mathematics is very important subject for all branches of Study. Now the challenge is how it can be very easy to take this subject. In this book theory of mathematics has been discussed. If we are very about the theory then it's not a problem to solve the problem. This no book can read as you are at home or traveling some where. My contribution to make mathematics easy for Class XI, Class XII and Joint Entrance Examination aspirants.
